The improved resolution of laser-based angle-resolved photoemission spectroscopy (ARPES) allows reliable access to fine structures in the spectrum. We present a systematic, doping-dependent study of a recently discovered low-energy kink in the nodal dispersion of Bi{sub 2}Sr{sub 2}CaCu{sub 2}O{sub 8+{delta}} (Bi-2212), which demonstrates the ubiquity and robustness of this kink in underdoped Bi-2212. The renormalization of the nodal velocity due to this kink becomes stronger with underdoping, revealing that the nodal Fermi velocity is non-universal, in contrast to assumed phenomenology. This is used together with laser-ARPES measurements of the gap velocity, v{sub 2}, to resolve discrepancies with thermal conductivity measurements

Vishik, I. M.

UNT Digital Library

Doping-dependent nodal Fermi velocity in Bi-2212 revealed by high-resolution ARPESI. M. Vishik,1, 2 W. S. Lee,1, 2 F. Schmitt,1, 2 B. Moritz,1, 2 T. Sasagawa,3 S.Uchida,4 K. Fujita,5 S. Ishida,4 C. Zhang,6 T. P. Devereaux,1, 2 and Z. X. Shen1, 21Stanford Institute for Materials and Energy Sciences,SLAC National Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, CA 94025, USA2Geballe Laboratory for Advanced Materials, Departments of Physicsand Applied Physics, Stanford University, Stanford, CA 94305, USA3Materials and Structures Laboratory, Tokyo Institute of Technology, Meguro-ku, Tokyo 152-8550, Japan4Department of Physics, Graduate School of Science,University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan5Laboratory for Atomic and Solid State Physics,Department of Physics, Cornell University, Ithaca, NY 14853, USA6State Key Laboratory of Crystal Materials, Shandong University, Jinan, 250100, P.R.China(Dated: March 23, 2010)The improved resolution of laser-based angle-resolved photoemission spectroscopy (ARPES) al-lows reliable access to fine structures in the spectrum. We present a systematic, doping-dependentstudy of a recently discovered low-energy kink in the nodal dispersion of Bi2Sr2CaCu2O8+δ (Bi-2212), which demonstrates the ubiquity and robustness of this kink in underdoped Bi-2212. Therenormalization of the nodal velocity due to this kink becomes stronger with underdoping, reveal-ing that the nodal Fermi velocity is non-universal, in contrast to assumed phenomenology. This isused together with laser-ARPES measurements of the gap velocity, v2, to resolve discrepancies withthermal conductivity measurements.PACS numbers:In a d -wave superconductor like the high-Tc cuprates,the electronic component of low-temperature thermo-dynamics is dictated by the nodes, where arbitrarilysmall excitations are permitted by the gapless natureof these points. An intriguing aspect of cuprate phe-nomenology is the so-called universal nodal Fermi ve-locity (vF ).[1] Along the nodal direction ((0,0)-(π,π))the velocity measured by ARPES within 50 meV ofEF appears to be independent of cuprate-family or thenumber of CuO2 layers in the compound, and is alsonearly constant across the phase diagram – from the un-doped insulator, across the superconducting dome, andin the non-superconducting metallic state at a dopingp>0.25 – even though other electronic properties varysignificantly with doping.[2–4] In addition, this univer-sal vF , if combined with ARPES measurement of thesuperconducting gap, leads to apparent contradictionwith thermal conductivity observed directly in transportmeasurements,[5, 6] suggesting that crucial informationabout the nodal quasiparticles is still missing.ARPES data can be represented as a convolutionbetween the single-particle spectral function and themomentum and energy resolution of the experiment.Naturally, with the improved resolution of laser-basedARPES, the measured spectrum begins to approach theintrinsic spectral function, and finer structure can be re-vealed. Recent laser-ARPES measurements along thenodal direction of optimally-doped Bi-2212 have uncov-ered a low-energy (<10 meV) kink,[7] in addition tothe larger kink seen at 50-80 meV in all cuprates.[8–10]Other laser-ARPES studies have shown a correspond-FIG. 1: (a)-(c) False-color image plots of the nodal dispersionof UD55, UD65, and UD92, measured at 10K. Solid curvesindicate band dispersions derived from MDC peak positions.Inset of (a): Brillouin zone schematic with Fermi surface in-dicated in red. The x -axes in (a)-(c) correspond to momen-tum along diagonal blue line (‘nodal cut’) in inset. (d) EDCs(solid) and symmetrized EDCs (dashed) at kF . A single peakat EF in the latter confirms that spectra in (a)-(c) are un-gapped. kF determined from Fermi crossing of dispersion(vertical dashed lines in (a)-(c)).ing decrease in nodal linewidth at low energies.[11–13]In this letter, we present the systematics of the low-energy kink by means of a doping-dependent study ofunderdoped Bi-2212. 20 samples with 6 dopings in therange 0.076<p<0.14 were measured using a 7 eV laserand a Scienta SES2002 analyzer. 7 eV photons wereproduced by second harmonic generation from a 355 nmlaser (Paladin, Coherent, Inc.) using a nonlinear crystalKBe2BO3F2.[14] Energy and momentum resolution were3 meV and better than 0.005 Å−1, respectively. Sam-SLAC-PUB-14085Work supported in part by US Department of Energy contract DE-AC02-76SF00515.2FIG. 2: (a) Band dispersions from Fig 1, offset for clarity.Dashed line accompanying UD55 denotes assumed linear bareband. Black dotted lines are linear fits 30-40 meV (vmid),extrapolated to EF . This differs from vF (fit 0-7 meV), in-dicated on UD65 dispersion by orange dashed line. Pink barmarks 70 meV kink, and grey bar marks low-energy kink,where vF deviates from vmid. Inset: UD92 dispersion below20 meV. (b) ReΣ, approximated by subtracting a linear bareband from dispersions in (a), is peaked at the position of the70 meV kink and changes slope near the energy position ofthe low-energy kink. (c) Detail of the low-energy portion ofReΣ. Thick dotted lines are fits near EF . All curves devi-ate from these lines between 6-10 meV, as highlighted by theshaded bar. For the two most underdoped samples, the slopeof ReΣ evolves between the low-energy kink and 20-30 meV,suggesting an additional kink. (d) 2ImΣ, with dotted lines asguides-to-the-eye. All curves decrease more rapidly near EF ,but most markedly in UD92. For more underdoped samples,the effect may be obscured by a larger linewidth and possibleadditional kink.ples were cleaved in-situ at a pressure <4×10−11 torr toobtain a clean surface, and measured at 10K.Fig. 1(a)-(c) show ARPES image plots for nodal cutsat three dopings: UD55 (underdoped, Tc=55K), UD65,and UD92, corresponding to hole-dopings of approxi-mately 0.088, 0.10, and 0.14. Standard momentum dis-tribution curve (MDC) analysis–Lorentzian fits at fixedenergy– is used to extract the band dispersions.[15] Theenergy distribution curves (EDCs)–intensity as a func-tion of energy at fixed momentum– at kF in Fig. 1(d)indicate that these spectra are ungapped, as the sym-metrized EDCs [16] have a single peak at EF .The systematics of the low-energy kink are studied viathe MDC-derived nodal dispersion, which are plotted forthree dopings in Fig. 2(a). In addition to the large,ubiquitous kink near 70 meV, a smaller kink is also evi-dent: the dispersion within 10 meV of EF deviates fromthe velocity fit between 30-40 meV. This deviation ap-pears more pronounced for more underdoped samples.Consistent with the work of Plumb et al, the velocity(slope of the MDC dispersion) within 7 meV of EF issmaller than the velocity at higher binding energy, no-tably opposite to the expected effects of instrument andthermal broadening.[7] We also note that the low-energykink cannot be identified as an artifact due to a gap, be-cause measurements are performed at the node where thesuperconducting gap is zero.Another way to visualize the low-energy kink is viathe real part of the electronic self-energy, ReΣ, plot-ted in Fig. 2(b)-(c). The low-energy kink is markedby a deviation of the slope of ReΣ at 6-10 meV fromthe slope established at EF . For the sample closest tooptimal doping, UD92, there is a single ‘knee’ in ReΣ.Meanwhile, the slope of ReΣ for UD55 and UD65 con-tinues to evolve until 20-30 meV, possibly suggesting anadditional kink, reminiscent of the 70meV kink, whichmay have several components.[17–19] From the Kramers-Kronig relation between ReΣ and ImΣ, a signature of thelow-energy kink is expected in ImΣ, which is proportionalto the MDC FWHM. In Fig. 2(d) we show that all dop-ings exhibit a downturn in ImΣ near EF , though this ismost pronounced for UD92. For more underdoped sam-ples, the larger linewidth and possible additional kinkmake it more difficult to get quantitative informationfrom ImΣ, but the observation that ImΣ decreases morerapidly close to EF remains robust. The appearance ofa low-energy feature in both ReΣ and ImΣ strongly ar-gues against a spurious origin for the low-energy kink,and the phenomenology reported in Fig. 2 is reproducedin the other samples in our study. Thus, the systematicsof a new energy scale can be added to the hierarchy ofmultiple energy scales in the cuprates.[20]The ubiquity of the low-energy kink in UD Bi-2212leads us to reexamine previous measurements of vF , asthere is now compelling evidence that quasiparticles veryclose to EF experience a heretofore unconsidered massrenormalization. The nodal vF is plotted in Fig. 3, andour key finding is that vF is not universal, but rather,has a pronounced doping dependence in the regime ofthis study. To characterize our data, at least two ve-locities are needed: vmid, the linear fit between 30-40meV, and vF , the velocity fit between 0-7 meV, as de-fined in Fig. 2(a). These energy ranges are chosen to getsufficient data points while avoiding the low-energy kinkand 70 meV kink. vmid is found to be approximately1.8 eVÅ, without a distinct doping dependence, con-sistent with the previously reported ‘universal’ value.[1]Meanwhile, vF decreases monotonically with underdop-ing. This is consistent with recent quantum oscillationresults, which suggest a divergence of the effective massin the underdoped regime.[21] The coupling strength of3FIG. 3: (a) Doping dependence of vF and vmid. Openred (blue) squares denote average vF (vmid) for each dop-ing. Boundary of shaded region denotes doping dependence ofTc. Doping is approximated from empirical relation Tc=96(1-82.6(p-0.16)2).[22] vmid has little systematic doping depen-dence, while vF decreases with underdoping. (b) Doping de-pendence of vmid/vF , which is related to the renormalizationcoupling strength.this low-energy renormalization can be roughly assessedby the velocity ratio vmid/vF , which is plotted in Fig.3(b), and suggests that coupling strength increases withunderdoping. Notably, the ratio of velocities on eitherside of the 70meV kink exhibits the same doping depen-dence, though with the 70 meV kink, it is the higher en-ergy velocity (ω>70meV) which is doping-dependent.[1]Although a doping-dependent vF presents a significantshift from our previous understanding of cuprate nodalphysics, our results are not inconsistent with previousmeasurements: vmid is indeed doping-independent, andinferior energy resolution can easily obscure subtle low-energy kinks near EF . Our finding underscores the im-portance of very low energy scales in these systems andrevises cuprate phenomenology by linking nodal vF todoping and Tc, previously suggested by the temperaturedependence of the low-energy kink.[7] Further, this dop-ing dependence constrains the origin of the low-energykink, and may aid interpretation of bulk thermodynamicmeasurements, particularly thermal conductivity, whichwill be the focus of the remaining discussion.For the cuprates, thermal conductivity near T=0 canbe expressed in terms of two components of the Fermivelocity: the velocity perpendicular to (vF ) and tan-gential to (v2) the Fermi surface (FS) at the node (Fig.4(a)-(c)).[23–25] For a 2D d -wave superconductor in theclean limit, the residual linear term (T=0 extrapola-tion) of thermal conductivity, κ0/T, is independent ofthe quasiparticle scattering rate, interaction energy, orother sample-dependent parameters.[24, 26]In this regime, κ0/T is related to vF and v2 by a simpleformula:[23, 24, 26]κ0/T =k2B3~nd[vFv2+v2vF], (1)where n is the number of CuO2 planes per unit cell,and d is the c-axis unit cell length. The second termis usually negligible, as v2vF . Thus, by measuringbulk thermal conductivity, one can extract a microscopicparameter, v2/vF , which fully determines the groundstate nodal electronic structure of cuprates.[25] Ther-mal conductivity measurements on La2−xSrxCuO4,[27,28] YBa2Cu3O7,[28] Bi2Sr2−xLaxCuO6+δ,[29] and Bi-2212[5] have all shown that κ0/T decreases with un-derdoping, implying that vF /v2 also decreases. How-ever, using v2 reported in Ref. [30] and a universal vF ,Sun et al argued that ARPES suggested a different dop-ing dependence of vF /v2. [5] Such contradictions havebeen attributed to disorder effects, such as electronic in-homogeneity [5] or disorder-induced magnetism,[6] butprevious analysis lacked a crucial component: a doping-dependent vF .For comparisons via Eqn. (1), we have obtained v2from laser-ARPES measurements of the momentum de-pendence of the superconducting gap near the node (Fig.4(d)), and these values are consistent with recently pub-lished data. [31, 32] Using these v2 together with vFfrom Fig. 3(a), we plot the ratio vF /v2 in Fig 4(f) along-side the thermal conductivity values reported by Sun etal.[5] The ARPES vF /v2 decrease strongly with under-doping, exhibiting a consistent trend with the thermalconductivity results for Bi-2212 as well as other cuprates.The vF /v2 derived from ARPES and thermal conductiv-ity differ in absolute value, and this may be related tothe in-plane anisotropy of thermal conductivity that hasbeen reported in Bi-2212 (κa 6=κb). [5, 33] The doping-dependent data in Ref. [5] were along the a-axis, whichhas a larger κ0/T, but the discrepancy in absolute valueof vF /v2 shown in Fig. 4 (f) may indicate that the b-axismay be the correct one to compare to ARPES. NotablyARPES does not observe in-plane anisotropy of nodalsingle particle parameters (vF and v2), so the anisotropyin thermal conductivity must have a different origin, suchas coexisting density-wave order.[34] Alternately, the dif-ference in absolute value of vF /v2 may suggest a propor-tionality constant of different origin is needed in Eqn. (1).Nevertheless, with the doping-dependent vF elucidatedby laser ARPES, we are able to reproduce the doping-dependence of κ0/T which is seen in multiple cupratefamilies.The superior resolution of laser ARPES allows accessto some of the lowest energy scales of high-Tc cuprates,and the findings may further constrain the microscopictheory of high-Tc superconductivity. With this pow-erful probe, we have been able to uncover the dopingdependence of a microscopic parameter, vF . A non-universal nodal Fermi velocity both answers old questionsand introduces new ones: discrepancies between doping-dependent ARPES and thermal conductivity measure-ments can be resolved, but there are new questions aboutthe origin of the low-energy kink, the explanation of its4FIG. 4: (a) Cutout showing FS (top) and dispersion perpendicular (vF , left) and tangential (v2, right) to FS at node, frommeasurement on UD92 at 10K. (b)-(c) Image plots showing measured vF and v2 directly. The latter image consists of EDCsat kF from many parallel cuts near the node. (d) Comparison of synchrotron- and laser-based ARPES measurements of thesuperconducting gap of UD92 around the FS. When the data in (d) is fit to a simple d-wave form, ∆(θ)=∆0cos(2θ) close tothe node, v2 ≈ 2∆0/kF , where kF is the distance from the node to (π,π). (e) v2 from synchrotron- and laser-based ARPESexperiments. (f) Comparison between vF /v2 from laser ARPES and thermal conductivity from Ref. [5]. Doping dependenceis consistent, though absolute values differ. Open squares indicate average laser ARPES values.doping and temperature dependence, and its role in su-perconductivity.We thank Profs. N. Nagaosa, J. Zaanen, and F.Ronning for helpful discussions. SSRL is operated bythe DOE Office of Basic Energy Science. This workis supported by DOE Office of Basic Energy Science,Division of Materials Science, with contracts DE-FG03-01ER45929-A001 and DE-AC02-76SF00515.[1] X. J. Zhou, T. Yoshida, A. Lanzara, P. V. Bogdanov,S. A. Kellar, K. M. Shen, W. L. Yang, F. Ronning,T. Sasagawa, T. Kakeshita, et al., Nature 423, 398(2003).[2] Y. Ando, S. Komiya, K. Segawa, S. Ono, and Y. Kurita,Phys. Rev. Lett. 93, 267001 (2004).[3] J. L. Tallon and J. W. Loram, Physica C: Superconduc-tivity 349, 53 (2001).[4] T. Yoshida, X. J. Zhou, D. H. Lu, S. Komiya, Y. Ando,H. Eisaki, T. Kakeshita, S. Uchida, Z. Hussain, Z.-X.Shen, et al., J. Phys.: Condens. Matter 19, 125209(2007).[5] X. F. Sun, S. Ono, Y. Abe, S. Komiya, K. Segawa, andY. Ando, Phys. Rev. Lett. 96, 017008 (2006).[6] B. M. Andersen and P. Hirschfeld, Phys. Rev. Lett. 100,257003 (2008).[7] N. C. Plumb, T. Reber, J. D. Koralek, Z. Sun, J. F. Dou-glas, K. Aiura, Y.and Oka, H. Eisaki, and D. S. Dessau,arXiv:0903.4900v3[cond-mat.supr-con] (2009).[8] A. Lanzara, P. V. Bogdanov, X. J. Zhou, S. A. Kellar,D. L. Feng, E. D. Lu, T. Yoshida, H. Eisaki, A. Fujimori,K. Kishio, et al., Nature 412, 510 (2001).[9] P. Bogdanov, A. Lanzara, S. A. Kellar, X. J. Zhou, E. D.Lu, W. J. Zheng, G. Gu, J.-I. Shimoyama, K. Kishio,H. Ikeda, et al., Phys. Rev. Lett. 85, 2581 (2000).[10] X. J. Zhou, T. Cuk, T. Devereaux, N. Nagaosa, andZ.-X. Shen, in In Handbook of High-Temperature Super-conductivity, edited by J. R. Schrieffer and J. S. Brooks(Springer New York, 2007), pp. 87–144.[11] K. Ishizaka, T. Kiss, S. Izumi, M. Okawa, T. Shimo-jima, A. Chainani, T. Togashi, S. Watanabe, C.-T. Chen,X. Wang, et al., Phys. Rev. B 77, 064522 (2008).[12] W. Zhang, G. Liu, L. Zhao, H. Liu, J. Meng, X. Dong,W. Lu, J. S. Wen, Z. J. Xu, G. D. Gu, et al., Phys. Rev.Lett. 100, 107002 (2008).[13] J. D. Rameau, H.-B. Yang, G. D. Gu, and P. D. Johnson,Phys. Rev. B 80, 184513 (2009).[14] G. Liu, G. Wang, Y. Zhu, H. Zhang, G. Zhang, X. Wang,Y. Zhou, W. Zhang, H. Liu, L. Zhao, et al., Rev. Sci.Instrum 79, 023105 (2008).[15] P. D. Johnson, A. V. Fedorov, and T. Valla, J. ElectronSpectrosc. Relat. Phenom. 117-118, 153 (2001).[16] M. R. Norman, M. Randeria, H. Ding, and J. C. Cam-puzano, Phys. Rev. B 57, R11093 (1998).[17] W. S. Lee, W. Meevasana, S. Johnston, D. H. Lu, I. M.Vishik, R. G. Moore, H. Eisaki, N. Kaneko, T. P. De-vereaux, and Z.-X. Shen, Phys. Rev. B 77, 140504(R)(2008).[18] W. S. Lee, S. Johnston, T. P. Devereaux, and Z.-X. Shen,Phys. Rev. B 75, 195116 (2007).[19] X. J. Zhou, J. Shi, T. Yoshida, T. Cuk, W. L. Yang,V. Brouet, J. Nakamura, N. Mannella, S. Komiya,Y. Ando, et al., Phys. Rev. Lett. 95, 117001 (2005).5[20] W. Meevasana, X. J. Zhou, S. Sahrakorpi, W. S. Lee,W. L. Yang, K. Tanaka, N. Mannella, T. Yoshida, D. H.Lu, Y. L. Chen, et al., Phys. Rev. B 75, 174506 (2007).[21] S. E. Sebastian, N. Harrison, M. M. Altarawneh, C. H.Mielke, R. Liang, D. A. Bonn, W. N. Hardy, and G. G.Lonzarich, arXiv:0910.2359v1 [cond-mat.str-el] (2009).[22] J. L. Tallon, C. Bernhard, H. Shaked, R. L. Hitterman,and J. D. Jorgensen, Phys. Rev. B 51, 12911 (1995).[23] M. Chiao, R. W. Hill, C. Lupien, L. Taillefer, P. Lam-bert, R. Gagnon, and P. Fournier, Phys. Rev. B 62, 3554(2000).[24] N. E. Hussey, Adv. Phys 51, 1685 (2002).[25] H. Shakeripour, C. Petrovic, and L. Taillefer, New Jour-nal of Physics 11, 055065 (2009).[26] A. C. Durst and P. A. Lee, Phys. Rev. B 62, 1270 (2000).[27] J. Takeya, Y. Ando, S. Komiya, and X. F. Sun, Phys.Rev. Lett. 88, 077001 (2002).[28] M. Sutherland, D. G. Hawthorn, R. W. Hill, F. Ron-ning, S. Wakimoto, H. Zhang, C. Proust, E. Boaknin,C. Lupien, L. Taillefer, et al., Phys. Rev. B 67, 174520(2003).[29] Y. Ando, S. Ono, X. F. Sun, J. Takeya, F. F. Balakirev,J. B. Betts, and G. S. Boebinger, Phys. Rev. Lett. 92,247004 (2004).[30] J. Mesot, M. R. Norman, H. Ding, M. Randeria, J. C.Campuzano, A. Paramekanti, H. M. Fretwell, A. Kamin-ski, T. Takeuchi, T. Yokoya, et al., Phys. Rev. Lett. 83,840 (1999).[31] K. Tanaka, W. S. Lee, D. H. Lu, A. Fujimori, T. Fujii,Risdiana, I. Terasaki, D. J. Scalapino, T. P. Devereaux,Z. Hussain, et al., Science 314, 1910 (2006).[32] W. S. Lee, I. M. Vishik, K. Tanaka, D. H. Lu,T. Sasagawa, N. Nagaosa, T. P. Devereaux, Z. Hussain,and Z.-X. Shen, Nature 450, 81 (2007).[33] Y. Ando, J. Takeya, Y. Abe, X. F. Sun, and A. N. Lavrov,Phys. Rev. Lett. 88, 147004 (2002).[34] P. R. Schiff and A. C. Durst, arXiv:0908.3168v1[cond-mat.supr-con] (2009).

Doping-Dependent Nodal Fermi Velocity in Bi-2212 Revealed by High-Resolution ARPES

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Doping-Dependent Nodal Fermi Velocity in Bi-2212 Revealed by High-Resolution ARPES

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